Multifunctional redundancy: Impossible or undetected?

Abstract The diversity‐functioning relationship is a pillar of ecology. Two significant concepts have emerged from this relationship: redundancy, the asymptotic relationship between diversity and functioning, and multifunctionality, a monotonic relationship between diversity and multiple functions occurring simultaneously. However, multifunctional redundancy, an asymptotic relationship between diversity and multiple functions occurring simultaneously, is rarely detected in research. Here we assess whether this lack of detection is due to its true rarity, or due to systematic research error. We discuss how inconsistencies in the use of terms such as ‘function’ lead to mismatched research. We consider the different techniques used to calculate multifunctionality and point out a rarely considered issue: how determining a function's maximum rate affects multifunctionality metrics. Lastly, we critique how a lack of consideration of multitrophic, spatiotemporal, interactions and community assembly processes in designed experiments significantly reduces the likelihood of detecting multifunctional redundancy. Multifunctionality research up to this stage has made significant contributions to our understanding of the diversity‐functioning relationship, and we believe that multifunctional redundancy is detectable with the use of appropriate methodologies.

rate of functioning. The asymptotic relationship between diversity and ecosystem functions gives rise to an additional crucial concept: redundancy (Box 1; Fetzer et al., 2015;Galland et al., 2020). If diversity can increase without altering the rate of a particular ecosystem function once a threshold has been reached, then it must also be possible for diversity to decrease without any change in the rate of that function, provided diversity is maintained above a critical level. This implies that highly diverse ecosystems possess some form of redundancy within their communities such that losing one or more species does not alter the rate of a given ecosystem process. Redundancy can be considered through multiple lenses, such as species diversity or functional diversity (Box 1). A trait-based functional approach has a stronger mechanistic backing (Box 1, Mori et al., 2013) but is more difficult to assess due to higher information requirements.
Organisms are multifunctional because their activities influence the rate of several ecosystem functions simultaneously (e.g. plants fix carbon, transpire water and cycle nutrients) Consequently, it is possible that the loss of a particular species might differentially impact the rates of several processes, which undermines the concept of redundancy (Mori et al., 2013). In response, 'ecosystem multifunctionality' was coined to describe the relationship between diversity and the simultaneous operation of multiple functions (Hector & Bagchi, 2007), with multiple studies implying a nonasymptotic relationship between diversity and the number of functions performed in a community Mori et al., 2016;Peter et al., 2011). However, it is also possible that multiple functions can be maintained within the ecosystem despite the loss of species: thus, ecosystems could possess multifunctional redundancy. Currently, the field tends towards the thinking that 'low multifunctional redundancy' (i.e. no multifunctional redundancy, Box 1, Mori et al., 2013) occurs in ecosystems because the relative contributions of different species to multiple functions changes over time, meaning no species are redundant (see also Hillebrand & Matthiessen, 2009).
Multifunctional redundancy is more challenging to detect than redundancy for a single function. Although redundancy among species performing single functions is often observed (Balvanera et al., 2006), multifunctional redundancy appears rare in both designed experiments and surveys (Li et al., 2021). A meta-analysis by Hillebrand and Kunze (2020) found that ecosystems typically recover from disturbances, with higher recovery of ecosystem functioning compared to ecosystem composition. They implied that functional redundancy is of key importance here-we argue that because ecosystems are multifunctional, a mechanism underlying recovery could be multifunctional redundancy.
Despite this assertion, we question whether multifunctional redundancy exists or whether methodological problems prevent its detection. We found that the sheer variety in methods and terminology precluded a formal systematic review or meta-analysis. Instead, we have evaluated two broad fields in multifunctionality research: methods and ecological complexities, and provide insights into how we can move past the current issues in the field. Hector and Bagchi (2007) pioneered multifunctionality research by suggesting that species potentially redundant in the context of a single function may not be redundant when more functions are considered. They found a positive, asymptotic relationship between species richness and the number of functions measured, that is, that species differentially affect processes, and, therefore, multiple species are required to maintain ecosystems. This relationship was discovered in a long-term experiment consisting of randomly assembled plant communities, and involved multiple community attributes that were not necessarily functions (e.g. above and below ground biomass, nitrogen pools: Spehn et al., 2005). Multifunctionality was subsequently investigated by  across three communities, finding that functional redundancy was much lower when multiple functions were considered simultaneously compared to single functions. These researchers used different methods of measuring multifunctionality, measured different functions and used functional maxima calculations from monoculture studies (Hillebrand & Matthiessen, 2009), making them difficult to compare despite outward facing similarities. Following from here, multiple researchers failed to detect an asymptotic relationship between multifunctionality and diversity (Maestre et al., 2012;Zavaleta et al., 2010), leading to the concept of low multifunctional redundancy (Box 1). However, these later works are still difficult to compare due to the variety of methods available to calculate multifunctionality.

| Calculating multifunctionality
Multifunctionality can be calculated using multiple methods (Byrnes et al., 2014(Byrnes et al., , 2022Eskelinen et al., 2020), impeding the development of a universally applicable metric. Most of the conceptual development and early empirical studies of multifunctionality retrofitted results from large-scale, designed experiments such as BIODEPTH (e.g. Gamfeldt & Roger, 2017;Hector & Bagchi, 2007). Several methods were used to retroactively calculate multifunctionality from individually measured functions. Rather than discuss these common methods here, see the comprehensive prior discussion on the four most common ways to measure multifunctionality by Byrnes et al. (2014): the 'single-function', averaging, turnover, and singlethreshold approaches. Instead, we will be describing novel methods of measuring multifunctionality, and how we need to treat our data and methods moving forward in multifunctionality research. Byrnes et al. (2014) introduced an extension of the threshold approach, which computes the number of functions performing at or above each of multiple thresholds and regressing these values against species richness. Van Der Plas et al. (2016) successfully used this method to quantify multifunctionality in naturally assembled European tree communities. They found a positive relationship BOX 1 Diversity, redundancy and multifunctionality.

Redundancy (A) Multifunctional redundancy
Species redundancy is an asymptotic relationship between species richness and the rate of an individual function (Walker 1992). Mechanisms underlying single function redundancy include the portfolio effect, the effect that variance in ecosystem function declines with decreasing species richness (Doak et al. 1998), the insurance hypothesis, that alongside the portfolio effect, asynchrony in species responses reduces variation in ecosystem function (Yachi & Loreau 1999), and overyielding, where productivity increases with species richness (Tilman 1999). An alternative to species redundancy is functional redundancy, an asymptotic relationship between functional diversity and the rate of an individual function (Fetzer et al. 2015).
Researchers have recently assessed redundancy through a trait-based approach where communities containing species with the same effect traits (those that influence ecosystem function) but multiple response traits (i.e. those that respond to environmental change) lead to the maintenance of a function under different stressors (e.g. Mori et al. 2013, Galland et al. 2020).
Multifunctional redundancy is an asymptotic relationship between the number of species and/or amount of functional diversity. "Low multifunctional redundancy" (B) (Mori et al. 2013), asserts that the number of species required to maintain multifunctionality increases as ecosystems become more complex (e.g. spatiotemporal differences). "High multifunctional redundancy" (C) has been observed by Wang et al. 2021, and is an asymptotic relationship between the number of species occurring in a community and multiple ecosystem functions occurring simultaneously.
between species richness and multifunctionality at low thresholds, peaking when all functions were performing at 37% of their maximum rate, implying multifunctional redundancy was occurring at moderate thresholds. The same analysis, however, also found that the relationship between species richness and multifunctionality became negative when functions were being performed at 76% of their maximum rate. Van Der Plas et al. (2016) suggested that this was true because performing functions at very high rates may compromise the performance of other functions. Overall, using Byrne's novel metric, multifunctional redundancy was detectable at moderate thresholds.
Novel metrics have also been proposed. found that biodiversity-multifunctionality relationships differed depending on the method used, suggesting that some outcomes may be driven more by the method used to analyse data, as opposed to the data itself. This makes it exceptionally difficult for researchers to know if their result is due to an artefact of the method they used, or a true result! Gamfeldt and Roger (2017) emphasised this, noting that seemingly trivial decisions about the choice of technique or threshold impacts research findings.

| Inconsistent terminology
An ecosystem function is the flow of materials and processing of energy (Naeem, 2008)  functional maximum through facilitation compared to a researcherassembled community. Every community will have a slightly different reference maximum, thus designing experiments around the concept of a functional reference maximum will assist the production of accurate estimates of multifunctionality. This will likely involve taking a multifunctionality measurement, manipulating the community somehow, and retaking the measurement to see if multifunctionality was altered in order to ensure that relative functional maxima are compared between different communities (Box 2).

| Measuring biomass versus rates
Many studies use biomass as a proxy for rate-based measurements of functions (e.g. Moi et al., 2021), which may obscure redundancy relationships. For example, aquatic food webs often have inverted pyramids of biomass due to the shorter generation times of plankton compared to their consumers (Mccauley et al., 2018). This means that biomass pools cannot be maximised simultaneously. If such biomass pools are used as proxies for rate, multifunctional redundancy cannot be achieved as there is no ability for multiple biomass pools to asymptote simultaneously.
Recasting such food webs in terms of production re-establishes the pyramidal shape (Mccauley et al., 2018). In order to use biomass as a proxy for a function, correlations between biomass and a rate must be established (e.g. Garland et al., 2021) otherwise functioning cannot be maximised and incorrect values are used in analyses, (e.g. Box 2), potentially altering the observed relationship between diversity and multifunctionality. Parallel functions are those that are driven by independent processes. However, parallel functions can have the same response.

| Correlated functions
For example, transpiration and gross primary productivity are independent processes, but both respond to light and water availability (Jones, 2013). If parallel functions are positively correlated and contained within a single species, multifunctional redundancy will be lower, because adding or removing such a species results respectively increases or decreases multifunctionality. By contrast, if the parallel functions are negatively correlated and contained within the same species, such as wood rotting processes where carbon sequestration declines as decomposition increases, multifunctional redundancy could be neutrally affected. The rates of parallel functions may also change based on environmental changes, for example, Küpper et al. (2008) found that when iron is limited in a marine cyanobacterium, nitrogen fixation is reduced but photosynthetic rates are maintained, which both means that not only species loss, but physiological changes in individuals are important, leading to complex relationships. Overall, rather than attempting to incorporate these complexities into experiments, the way we perform experiments to determine multifunctionality could assist in incorporating these complexities while reducing our need to directly consider them while selecting functions to measure. It is worth noting that negative correlations within a single species are rare, and therefore may not affect multifunctionality metrics. Calculating metrics from reference maxima will also allow us to incorporate these correlated functions, without having to fully understand them.

| Multitrophic complexities
Multifunctionality studies often occur within a single trophic level (e.g. Hector & Bagchi, 2007), thus simplifying ecosystem complexities. Lefcheck et al. (2015) concluded that confining multifunctionality test to a single trophic level may underestimate biodiversity effects on multifunctionality. They substantiated this by studying multitrophic multifunctionality in many one-to three-species systems, and found that the effect of biodiversity on multifunctionality increased both when more functions were considered and when the effect of diversity on multifunctionality was considered at higher trophic levels over lower ones. Soliveres et al. (2016) analysed data from 150 grasslands, across multiple trophic levels from soil microbes through to grazers and predators, finding that multifunctionality was highest when multiple trophic groups were considered over a single functional group.
They studied ecosystem services over ecosystem functions in their calculation of the multifunctionality metric, and used multiple single-threshold tests of multifunctionality in their analysis. This consideration of multiple trophic levels is important in multifunctionality research; however, issues with the type of functions being measured may be preventing the detection of high multifunctional redundancy.

| Spatiotemporal complexities
It is possible for species to coexist in space but not in time or vice versa. Accordingly, there are trade-offs between different functions, meaning that relationships between biodiversity and multifunctionality are highly complex (Hillebrand & Matthiessen, 2009). Mori et al. (2018) pointed out that all such studies thus far have considered α-diversity loss, but loss of β-diversity is also important due to spatial complexity because we cannot expect all functions to reach their maxima in one location due to functional trade-offs. Many multifunctionality studies only consider one level of spatial and temporal complexity (e.g. Bradford et al., 2014;Hector & Bagchi, 2007;Peter et al., 2011), and do not consider this spatial turnover. Using different vegetation layers, Wang et al. (2021) compared multifunctionality over different spatial scales, finding that multifunctionality varied spatially, meaning that spatiotemporal complexity is important to consider in multifunctionality studies. Furthermore, asynchronous biomass production of co-occurring grassland species led to a high degree of temporal stability in productivity at the community level (Ma et al., 2017), demonstrating how important it is to consider whole ecosystems over space and time when calculating multifunctionality.

| Community assembly processes, interactions and redundancy
Community assembly processes develop key biotic and abiotic interactions underlying redundancy. As early as 1980, Yodzis (1980) found that deterministic community assembly processes are important for developing paired species interactions. This was exemplified in a study of the effects of random versus non-random extinctions of marine invertebrates on bioturbation which found that non-random extinctions reduced bioturbation more than random extinctions (Solan, 2004). In the 1990s, as redundancy was being explored, species linkages and interactions were identified as key drivers underlying redundancy (Doak et al., 1998;Johnson et al., 1996;Lawton & Brown, 1994;Yachi & Loreau, 1999). Despite not explicitly using the term 'redundancy' and using an artificially created community, Downing et al. (2014) used a zooplankton experiment to find that weak interactions reduced population variability in 'variable' environments, implying that weak interactions may have a key role in redundancy.
Despite these clear connections between community assembly, species interactions and redundancy, community assembly processes are often ignored in multifunctionality research. For example, the BIODEPTH project design, which has been used by later studies of multifunctionality (e.g. Gamfeldt & Roger, 2017) randomly selected species from different functional groups to produce experimental communities of different biological and functional diversities (Spehn et al., 2005). Furthermore, Slade et al. (2017) studied the relationship between diversity, interspecies interactions and multifunctionality in dung beetle communities and found that species interactions can increase or decrease functions. Meyer et al. (2018) found that multifunctionality increased with biodiversity but was limited by negative correlations between functions. Multifunctionality was also more limited when the environment was altered rather than when species composition was altered. The role of community assembly, taxonomic composition and functional trait composition on multifunctionality was reviewed by Butterfield et al. (2016). They used community average trait values, capturing the idea that the most dominant species in a system contributes the most to a trait class (e.g. body size) and drives the average quantitative value of that trait.
Their synthesis concluded that community assembly determines whether community average trait values or functional diversity drive multifunctionality processes.
Overall, in multifunctionality research, the dearth of communities developed by community assembly processes could significantly hamper our ability to detect multifunctional redundancy. Designing diversity-multifunctionality experiments that incorporate community assembly processes will be key to increasing the possibility of detecting multifunctional redundancy, as well as giving us a more realistic understanding of multifunctionality. soil. This selectively removed certain species, confirming that species loss was non-random. They left these samples for 60 days to ensure overall community abundance was the same despite variations in diversity. The functions they selected were measurable as rates (respiration, nitrogen fixation, nitrification and breakdown of organic material) and they calculated multifunctionality using the averaging technique. Overall, they found that species loss reduced multifunctionality more in the lower diversity site than in the higher diversity site, implying that high multifunctional redundancy occurred when soil diversity was higher. They then compared functional redundancy between sites, finding that the higher diversity soil had more taxa attributed to each functional group compared to the lower diversity soil, suggesting that functional group redundancy led to these results. Furthermore, when they analysed each function individually, they found that functions with the highest diversity among contributors were the most likely to show redundancy, whereas functions that relied on a smaller number of highly specialised taxa had significantly lower process rates, especially in the lower diversity soil. This study implies that when natural communities are manipulated with true ecosystem functions measured, high multifunctional redundancy is possible to detect, and, as we refine our methods further, we should be able to find other instances of high multifunctional redundancy.

| Consequences of using inappropriate methods
Clearly, using inappropriate methods to examine the relationship between diversity and multifunctionality may lead to artefacts.
Often, researchers studying the effects of biodiversity on functions randomly delete species and compare the resulting ecosystem function with its prior value or with that from a monoculture treatment. For example, Gamfeldt and Roger (2017), Hector and Bagchi (2007) and Jing et al. (2020) used BIODEPTH data to study multifunctionality, which used randomly selected subsets of species from functional groups to generate communities (Spehn et al., 2005). This approach would underestimate any relationships between diversity and functioning as they would be more likely to be an artefact of the experimental design, rather than of ecological mechanisms. Species losses from real perturbations are unlikely to be random. Environmental changes often selectively remove a suite of species that share certain response traits. For example, Solan (2004) found that random removal of marine invertebrates resulted in slower loss of a function (bioturbation) than if species were removed non-randomly, and Larsen et al. (2005) found that larger bodied bumble bees and dung beetles were both more extinction prone and more functionally efficient, meaning that species loss was non-random and resulted in greater loss of functional stability. Furthermore, when these response traits are correlated with effect traits, function loss occurs faster than when traits are uncorrelated (Solan, 2004) leading to lower functional redundancy. The observation that non-random species loss affects functioning more than random species loss has implications for many multifunctionality studies.

| How to progress
In order to progress multifunctionality research, there are key areas that need to be addressed. Here we outline each of these areas in turn.

| Definitions
To improve the chance of detecting high multifunctional redun-

| Experiments on natural versus constructed communities
Manipulating naturally assembled communities instead of constructing them is required for truly measuring multifunctionality.
Constructed communities are ideal for measuring individual functions (Marquard, Weigelt, Temperton, et al., 2009), and have led to significant development in the biodiversity-functioning space (Allan et al., 2011;Roscher et al., 2012). However, as we move forward in the investigations of biodiversity-functioning relationships, we must acknowledge that we do not fully understand the complexities of natural ecosystems from their formation through to current drivers of stability. We can still perform tests and studies to understand underlying mechanisms, but these tests must begin with a full, natural ecosystem that we can manipulate to remove species or change abiotic conditions.
Repurposing experiments originally designed for measuring single functions may hide multifunctional redundancy. Experiments in natural systems incorporate complexities (e.g. soil microbial systems) and the weak and the strong biotic and abiotic interactions that are key for redundancy relationships. The outcomes of these studies will undoubtedly contain unexplained variation due to unknown mechanisms, but will allow us to focus on mechanisms underlying these responses, and better understand natural systems (Box 3; Pinheiro et al., 2022).

| CON CLUS ION
Multifunctionality research up to this point has allowed us to expand our understanding of the complexity of biodiversity-ecosystem functioning relationships. However, to untangle it, further we must tread carefully through the web of existing methodology to design appropriate studies. Multifunctional redundancy is intuitively appealing but has been exceptionally difficult to detect given the rigidity and complexity of work required to achieve this. Nevertheless, understanding multifunctional redundancy is crucial for ecosystem management, particularly because it allows us to continue answering the question: why is diversity important? Moreover, it gives us meaningful insights into questions such as: how much diversity can we afford to lose?

AUTH O R CO NTR I B UTI O N S
Bridget E. White: Conceptualization (lead); writing -original draft (lead); writing -review and editing (equal). Mark J.

ACK N OWLED G M ENTS
We benefitted from discussions with Professor Belinda Robson Biodiversity-functioning studies can range from experimenting on structured species assemblages (top row) through to observing communities without manipulations (fourth row). Studies can be considered in vitro (top two rows), where species or whole communities are manipulated in a laboratory, glasshouse or mesocosm, or in vivo (bottom two rows), where communities are either manipulated or observed in the field. Experimental manipulations are key for exploring mechanisms underlying biodiversity-functioning relationships, and manipulations on communities that have experienced community assembly processes will give us a greater understanding of how functioning responds to biodiversity alterations.
and Bridget White has additional scholarship support from the University of Tasmania Research Training Program.

CO N FLI C T O F I NTE R E S T S TATE M E NT
The authors declare no competing interests.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data sharing is not applicable to this article as no new data were created or analysed in this study.